Particle motion associated with wave function density gradients

We study the quantum mechanical motion of massive particles in a system of two coupled waveguide potentials, where the population transfer between the waveguides effectively acts as a clock and allows particle velocities to be determined. Application of this scheme to evanescent phenomena at a reflective step potential reveals an energy-velocity relationship for classically forbidden motion. Regions of gain and loss, as described by imaginary potentials, are shown to speed up the motion of particles. We argue that phase and density gradients in quantum mechanical wave functions play complementary roles in indicating the speed of particles.Comment: 6 pages, 4 figure

Controllable Josephson junction for photon Bose-Einstein condensates

Josephson junctions are the basis for the most sensitive magnetic flux detectors, the definition of the unit volt by the Josephson voltage standard, and superconducting digital and quantum computing. They result from the coupling of two coherent quantum states, as they occur in superconductors, superfluids, atomic Bose-Einstein condensates, and exciton-polariton condensates. In their ground state, Josephson junctions are characterised by an intrinsic phase jump. Controlling this phase jump is fundamental for applications in computing. Here, we experimentally demonstrate controllable phase relations between photon Bose-Einstein condensates resulting from particle exchange in a thermo-optically tunable potential landscape. Our experiment realises an optical analogue of a controllable 0,$\pi$-Josephson junction. By connecting several junctions, we can study a reconfigurable 4-condensate system demonstrating the potential of our approach for analog spin glass simulation. More generally, the combination of static and dynamic nanostructuring techniques introduced in our work offers a powerful platform for the implementation of adaptive optical systems for paraxial light in and outside of thermal equilibrium.Comment: 21 pages, 5 figure

Inverse problems for microcavity tilt readout

Inverse problems in physics involve deducing system causes from observed effects, presenting challenges due to potential ill-posedness. Regularization techniques, addressing errors and instability, are vital in solving these problems, often combining analytical and numerical methods.In this work we want to inversely solve a Schrödinger equation to deduce the potential inside an optical microcavity. We apply this method to read out and stabilize the angular orientation of the two mirrors comprising an optical microcavity.To do so we observe mode patterns inside the microcavity and utilize key properties of the Schrödinger equation. We introducing and compare different regularization methods for efficacy assessment.</div

Unveiling Hidden Dynamics: Speed Measurements of Classically Forbidden Motion

For nearly a century, quantum tunneling has been a subject of sustained scientific interest. In a prior investigation [1], we introduced an unconventional method to explore evanescent phenomena at step potentials by examining particle motion within a system of coupled waveguides. In this system, the transfer of particles between waveguides serves as a clock, facilitating the determination of particle speeds even in classically forbidden regions. We implement this idea for photons in optical microcavity, which has full experimental access to the wave function. Using a novel nanostructuring method [2], we can guide photons in diverse potential landscapes, specifically within a coupled waveguiding structure. We measure particle speeds both in classically allowed and forbidden regions. Notably, our measurements show that classically forbidden regions speed up the motion of photons. Furthermore, our observations emphasize the significance of density gradients in wave functions for the motion of particles. We hope, these outcomes will provide valuable insights into the intricate dynamics of quantum tunneling phenomena, in particular make useful contribution to the tunneling time debate. Moreover, our findings can be viewed as a test of Bohmian trajectories in quantum mechanics.[1] Klaers, J., Sharoglazova, V., &amp; Toebes, C. (2023). Physical Review A, 107(5), 052201.[2] Vretenar, M., Puplauskis, M., Klaers, J.. Adv. Optical Mater. 2023, 2202820

Inverse problems for microcavity tilt readout

In paraxial approximation, the electromagnetic eigenmodes inside an optical microresonator can be derived from a Schrödinger-type eigenvalue problem [2,3]. In this framework, tilting the cavity mirrors effectively introduces a linear potential to the system. In our work, we apply solution strategies for inverse problems to precisely determine and control the relative orientation of two mirrors forming an optical microcavity. Our approach employs the inversion of the Schrödinger equation to reconstruct the effective potential landscape, and thus mirror tilts, from observed mode patterns. We investigate regularization techniques to address the ill-posed nature of inverse problems and to improve the stability of solutions. Our method consistently achieves an angle resolution of order 100 nanoradians per measurement.[2] D. Gloge and D. Marcuse, J. Opt. Soc. Am. 59, 1629 (1969).[3] C. Toebes, M. Vretenar, &amp; J. Klaers, Commun Phys 5, 59 (2022